Plenty of infrastructure especially those that have serious implications for public safety are equipped with sensors to monitor their performance and behaviors over time by providing real-time data and early warnings. Tilt sensors, a recent innovative advancement among various sensors, are crucial for intelligent monitoring in fields like structural health monitoring (SHM), due to their ability to measure and analyze precise tilt angle which is also a critical parameter in engineering disciplines. Tilt sensors have become instrumental components and they are widely used in various fields such as occupational medicine research, human movement tracking, underground drilling, geophysical observation, and construction^[1-7]. Tilt sensors effectively assess stability in structures by monitoring deviations and alerting engineers of potential hazards. Tilt sensors fundamentally offer insights into an object’s orientation for a given reference plane. Tilt sensors employ various sensing technologies to detect and measure angular displacement including accelerometers, pendulum systems, liquid-based mechanisms, cam structures, microelectromechanical systems (MEMS) technology, and cantilevers^[8-12]. These conventional tilt sensors rely on magnetic field variations to convert tilt angles into measurable electrical signals^[13] but they are highly susceptible to electromagnetic interference (EMI), waterproofing challenges, signal drifting, and long-term reliability problems^[14]. These vulnerabilities degrade the performance and measurement accuracy of the conventional sensors and it is necessary to address them.

Fiber Bragg Grating (FBG) technology as one of the many available optical fiber sensor techniques provides advantages over conventional sensors including immunity to EMI, small size, durability, and easy implementation of sensor arrays^[15]. FBGs are created by making periodic modulations in the refractive index in the core of an optical fiber. When light travels through this grating, a specific wavelength, known as the Bragg wavelength, experiences in-phase reflection due to the varying refractive index zones, leading to its amplification. FBG-based tilt sensors leverage the shift in the reflected light spectrum to achieve precise tilt measurements. This approach, based on light rather than electricity, offers inherent immunity to electromagnetic interference and temperature fluctuations, making these sensors exceptionally reliable in environments with high electrical noise or strong electromagnetic fields.

Over the past few decades, cantilever beam systems have become a well-established approach for fabricating FBG-based tilt sensors. With this type of FBG tilt sensor, mass blocks are attached to the cantilever beams, inducing strain on both the beam and the FBGs and eventually leading to measurable wavelength shifts. In 2015, Jiang etal.^[16] proposed an FBG tilt sensor comprised of three FBGs, two triangular cantilever beams, two weights, and a protective envelope. Two of the three FBGs are strain sensitivity elements and are marked as FBG1 and FBG2. The other one is used as a temperature compensation sensor. Brass was selected for the weights, which maximizes the influence of gravity on the pendulum. This gravitational influence subsequently induces deformation in the cantilever beam, constructed from a carbon fiber composite board. The prototype was tested in the laboratory with tilt angles ranging from −30 to 30 and having a sensitivity of 9.9 pm/°. In 2011, Ma etal.^[17] developed a proposed tilt sensor design utilizing a uniform-cross-section beam. A single bare FBG sensor was adhesively bonded to the top surface of the beam’s central axis. A pendulum was suspended in front of the beam through a free rotational joint. The pendulum’s movement due to tilt induced a concentrated gravitational force on the beam, resulting in strain on the surface directly measured by the FBG. It measured a sensitivity of 16.17 pm/° over a tilt angle range of −45° to 45°. In 2019, Liang etal.^[18] developed an FBG tilt sensor for posture monitoring of hydraulic supports in coal mine working face. The sensor consisted of a heavy ball, a pendulum, and two beams of uniform strength, with two FBGs bonded to the surfaces of the second beam to measure tilt angles with enhanced sensitivity while mitigating temperature cross-sensitivity. An additional FBG on the first beam measured angles in another dimension. The system demonstrated a sensitivity of 32.4 pm/° and a linear fitting coefficient of 0.9992 within a tilt range of −30° to 30°. Although the system exhibited good repeatability, the sensitivity is low. In 2015, a novel pendulum-based FBG 2-D tilt sensor was designed and demonstrated through an experiment by Yang etal.^[19]. The approach enables simultaneous measurement of applied 2D tilt angle and temperature variations through analysis of wavelength shifts in the two halves of each FBG. Experiments produced a maximum tilt angle sensitivity of 74 pm/° within the tilt angle range of 0° to 40°.

However, these cantilevers and pendulum-based tilt sensors mentioned above have their FBGs fixed to the cantilever beams close to the neutral axis. These FBGs tend to experience low sensitivity and precision. This limitation arises because, in static mechanics, it is stated that the strain is zero at the neutral axis of a bending beam^[20]. This principle states that the layer of material located at the neutral axis experiences no change in length when the beam deforms due to bending. As we move away from the neutral axis, the material experiences increasing levels of strain due to stretching on one side and compression on the other.

In our previous work [21], a sensitivity-enhanced tilt sensor based on femtosecond inscription technology FBG was developed. The enhanced sensitivity of the tilt sensor was achieved by designing a configuration where two FBG positions were displaced linearly away from the neutral axis of the cantilever beam. This displacement maximizes the strain component, resulting in improved sensitivity to tilt angles. The distance between the position of the FBGs and the neutral axis of the cantilever beam was set at 7.5 mm. This displacement maximizes the strain component hence improving the sensitivity of the tilt sensor. Experimental results show a sensitivity of 95.90 pm/° over a tilt angle range of −30° to 30° and a linearity of 99.94%. Although enhanced sensitivity has been achieved, further improvement and enhancement are necessary.

The primary objective of this current study is to optimize the structural design of the tilt sensor. Further improvement and enhancement in sensitivity are necessary especially for fields such as railway subgrade settlement and earthquake monitoring. Therefore, the sensitivity of the tilt sensor was enhanced by optimizing the structural design of the tilt sensor. Enhancing sensitivity is crucial for applications that demand precise tilt measurements. The optimized design builds upon the design established in our previous work, leveraging advanced methodologies to push the boundaries of sensor sensitivity. This paper details the steps taken in the optimization process, the methods used for testing the new design, and the results obtained, providing a thorough analysis of the improvements in sensor sensitivity and overall performance.

Fig. 1 (color online) illustrates the mechanical structure of the initial design. The sensor comprises a shell, a mass block, a cantilever, two FBGs, a shell cover, and a base. The base provides support for the shell, ensuring a secure attachment to the shell and the sensor application surface. The shell features access holes at the top and bottom to facilitate the passage of optical fibers. The cantilever is designed with three-holed in the upper section. The two holes on the outer positions in this upper section serve to mount the cantilever to the shell wall using screws. The lower section of the cantilever features two holes for threaded attachment of the mass block. The middle section of the cantilever acts as the elastic beam, and experiences strain induced by a mass block fastened to the lower section. Channels have been grooved to the middle layer of the beam on both the upper and lower sections of the cantilever to house the two FBG fibers, which are bonded to the middle layer of the cantilever using a high-temperature epoxy resin adhesive. The middle layer was selected for grooving as it provides a balance between strain sensitivity and mechanical protection. By positioning the FBGs slightly away from the neutral axis, the sensor can effectively detect both compressive and tensile strains, ensuring accurate and balanced measurements. This placement also offers mechanical protection to the FBGs, shielding them from external damage. Additionally, positioning the FBGs in the middle layer also contribute to greater stability under varying environmental conditions, helping to maintain sensor integrity in SHM applications. The assembled cantilever system is then housed within the aluminium shell and secured using the shell cover and screws. Prior to the design optimization study, finite element analysis (FEA) was conducted using SolidWorks simulation software to observe the strain distribution across the cantilever and FBGs when subjected to an applied force. The resulting equivalent strain distribution is shown in Fig. 2(a) (color online). The cantilever and mass were constructed from brass, and the FBGs were made of silica. Table 1 summarizes the material properties of both brass and silica. The analysis reveals that the surfaces of the beam and the FBGs where the force direction is applied experience the maximum strain while the rest of the cantilever experiences minimal strain as illustrated in Fig. 2(b) (color online).

As previously mentioned, in static mechanics, the strain at the neutral axis of a bending beam is theoretical. This principle states that the material layer at the neutral axis experiences no change in length as the beam bends. As we move away from the neutral axis, the material experiences increasing levels of strain due to stretching on one side and compression on the other. However, the theoretical model in static mechanics assumes ideal geometry and material properties whereas real-world scenarios exhibit slight imperfections. These imperfections can cause minor deviations from the perfectly linear relationship between strain and distance from the neutral axis, particularly near the axis itself where strains are very small. Therefore, to account for these imperfections, FEA was performed to investigate the optimal distance of the FBGs from the neutral axis that produces the maximum strain. Fig. 3 (color online) shows the labeled diagram of the cantilever showing the distance ($ {d}_{c} $) of the FBGs from the neutral axis, beam thickness $ t $, beam length $ L $, beam width $ h $, and $ h/2 $ representing the distance from the beam surface to middle layer of the beam and also the width of the channel.

To optimize the design and identify the distance that yields the maximum strain on the FBGs, a parametric finite element analysis (FEA) study was conducted. The distance ($ {d}_{c} $) was varied from 0.6 mm to 8.5 mm with a step of 0.1 mm. Simultaneously, the force value of 0.1 N to 1 N with a step of 0.1 N was applied to obtain the resulting maximum strain on the FBGs. The FEA simulation yielded a curvilinear graph, which is shown in Fig. 4(a) (color online). To provide a more intuitive representation of the graph, the data from 4.0 mm to 4.5 mm distance was amplified as shown in Fig. 4(b) (color online) and it can be observed that maximum strain occurs at a distance of 4.4 mm. These findings from the FEA simulations demonstrate that the distance of an FBG from the neutral axis of a beam has a greater influence in determining the value of its sensitivity. The graph shows that strain varies systematically with the distance from the neutral axis. At distances closer to the neutral axis, the strain value is relatively low, while it increases gradually as the distance increases. However, beyond a certain distance, the rate of increase in strain diminishes, indicating a saturation point. This occurs due to geometric stiffening, where increasing distance results in less additional strain being generated for the same applied force. This stiffening reduces the strain’s growth rate. Also, while strain ideally increases linearly with distance, larger distances introduce non-linearities in the beam’s bending behavior, causing strain to increase at a slower rate. Therefore, the 4.4 mm distance represents an optimal balance, where strain is maximized without compromising the sensor’s accuracy and the structure’s integrity. Similarly, the applied force influences the strain experienced by the sensor. Higher forces lead to increased strain, following a linear relationship. This observation highlights the importance of considering the magnitude of applied loads when designing and using the sensor. The FEA results highlight the importance of optimizing the sensor’s design parameters, such as distance from the neutral axis and structural strength, to maximize sensitivity and performance. According to the FEA results and engineering practice, 4.4 mm was selected to be the optimal distance of the FBG away from the neutral axis of the sensor beam while the other significant dimensions such as the length of the beam (L) and width of the beam (h) were maintained without compromising the size and integrity of the sensor.

However, modifications were made to the lower section of the cantilever design structure to ensure proper fit within the sensor shell, as illustrated in Fig. 5(a) (color online). The mass block structure was also redesigned to correspond with the new cantilever design, as shown in Fig. 5(b) (color online).

The prototype of the new sensor was designed with the following dimensions: $ {d}_{c} $= 4.4 mm, beam width ($ h $) = 4 mm, beam thickness ($ t $) = 1mm and beam length ($ L $) = 12 mm. For this experiment, the FBGs used were made with pure silica grating, which provides higher strength compared to conventional FBGs, and fabricated using a direct writing technique with a femtosecond laser operating at extremely short pulse durations in the femtosecond range (1 femtosecond = $ {10}^{-15} $ seconds). Initial laboratory tests show that these FBGs have a tensile limit exceeding 20 nm, while the stretching of our sensor is only about 4 nm. This level of stretching does not compromise the lifespan and performance of the FBGs. The specialized epoxy resin adhesive was used to securely bond the FBGs to the optimized cantilever of the sensor, followed by a high-temperature sealing process to ensure robust bonding. FBG1 has a reflectivity of 81.9%, a bandwidth of 0.29 nm, a side lobe suppression ratio (SLSR) of 27.7 dB, and a central wavelength of 1560 nm. FBG2 has a reflectivity of 71.8%, a bandwidth of 0.24 nm, an SLSR of 24.1 dB and a central wavelength of 1555.01 nm. The FBGs were then integrated with the cantilever and prestressed. The resulting prestressed central wavelength obtained were 1564.083 nm for FBG1 and 1559.159 nm for FBG2. Fig. 6 (color online) shows the physical sensor prototype fabricated.

Experiments were conducted in the laboratory under controlled environmental conditions. The sensor dimensions are 40 mm in length, 20 mm in width, and 65 mm in height. The mass block attached to the sensor weighed 135.6 g. The calibration system, as shown in Fig. 7 (color online), consists of an FBG interrogator, the tilt sensor, a personal computer (PC), a TLL90S dual-axis digital protractor with a high measuring accuracy of ±0.005°, and a rotatable platform fastened to a marble precision vibration isolation platform.

The FBG interrogator has a bandwidth range of 1525−1605 nm, an accuracy of 5 pm, an adjustable frequency range of 0−1000 Hz and a resolution of 0.1 pm.

During the experiments, the central wavelength shift was monitored by adjusting the tilt angles using the rotatable platform, which was securely fixed to the precision vibration isolation platform. A designated slot on the rotatable platform accommodated the dual-axis digital protractor for reading reference angles. The tilt sensor was mounted on top of the rotatable platform using bolts and connected to the FBG interrogator with a fiber optic jumper wire. The FBG interrogator recorded wavelength shift variations of the FBGs in real-time at a sampling frequency of 5 Hz.

The calibration process involved several steps. Firstly, the rotatable platform was adjusted to a stable state, allowing the wavelength to stabilize, and the wavelength corresponding to a tilt angle of 0° was recorded. Then, the calibration platform was rotated to −30°, after that systematically rotated gradually from −30° to 30° in 10° increments. The corresponding wavelength shift values were recorded at each tilt-stop point. To minimize errors caused by lag in changes, the system was held at each tilt point for 5 seconds before recording the data. The entire experimental process was repeated four times. Following the calibration experiments, the obtained data was analyzed. The wavelength shift at each tilt-stop point was recorded, and four linear fits were obtained from the four tests. The corresponding results of both FBG1 and FBG2 which were subjected to the same tilt angle range were assessed to determine their individual performance and depicted in Fig. 8(a) (color online) in terms of repeatability after the four tests. As evident from the graph, the two FBGs show a very good repeatability. In Fig. 8(b) (color online), the four curves obtained were averaged and plotted to also show the individual performance of the two FBGs. FBG1 exhibited a sensitivity of 64.35 pm/° over the tested tilt range. This indicates its high responsiveness to the applied tilt, translating tilt-induced strain effectively into a measurable wavelength shift. The linearity of FBG1 was also evaluated based on the coefficient of determination (R²), which was found to be 0.9996, showing a strong correlation between the tilt angle and the wavelength shift, consistent with the theoretical model. FBG2, positioned symmetrically to FBG1, demonstrated a sensitivity of 65.60 pm/°, slightly different from FBG1 due to its placement during assembly and mechanical interaction with the cantilever beam. FBG2 achieved a linearity of 0.9997, confirming that it also maintained a consistent and proportional response to the tilt angles applied. Since the FBGs are positioned symmetrically on either side of the neutral axis of the cantilever, their strain responses naturally oppose each other. When the cantilever bends due to a tilt, one FBG is subjected to tensile strain, which results in a positive wavelength shift, while the other experiences compressive strain, leading to a negative wavelength shift. Fig. 9(a) (color online) shows the wavelength shift difference of the two FBGs for the four tests, which also maintains good repeatability across the tilt angle range (error value < 0.94%).

Fig. 9(b) (color online) presents the linear fit obtained by averaging the values of the wavelength shift differences of FBG1 and FBG2 at each tilt stop point across the four test runs and compared to the initial design. The graph shows that the sensitivity of the optimized FBG tilt sensor within the −30° to 30° tilt angle range is calculated to be 129.95 pm/°. This increase in sensitivity is attributed to the optimized placement of the FBGs, which allows for more efficient capture of tilt-induced strain by maximizing the distance from the neutral axis. As a result, the sensor’s ability to detect smaller changes in tilt angle is significantly enhanced. The wavelength shifts difference between FBG1 and FBG2 are due to the opposing strain responses experienced by the two FBGs. These opposite strain responses allow the sensor to detect tilt with higher precision by leveraging the differential shifts between the two FBGs. In addition to the improvement in sensitivity, the graph also reveals a higher degree of linearity in the optimized design, with an R² value of 0.9997. The enhanced linearity contributes to the sensor’s reliability, making it more suitable for applications requiring precise tilt measurements. Table 2 provides a direct comparison between the initial and the optimized sensor designs in terms of sensitivity and linearity. The results demonstrate that the optimized sensor design offers a significant enhancement in both sensitivity and linearity, making it more adept at detecting and accurately measuring tilt angles. These improvements highlight the sensor’s potential for better performance and reliability in practical applications.

The creep performance test is conducted to measure the ability of the structure material to resist deformation under a constant tilt, as well as to evaluate how well the sensor maintains its accuracy over an extended period. The wavelength shift was recorded at 0° for 2 minutes and then tilted and securely fixed at 30° for 120 minutes. The rotatable platform was then swiftly returned to 0° and kept for another 2 minutes. The FBG interrogator collects the wavelength data of the FBGs in real-time at a sampling frequency of 5 Hz. The recorded wavelength shifts for the entire experiment were analyzed and depicted in Fig. 10 (color online). To provide a more intuitive representation of the sensor’s creep performance, the data from the 60 to 65 minutes timeframe was amplified. As illustrated in the graph, the FBG wavelength shift difference variation remained within 15 pm. This provides an additional indication that the tilt sensor has strong creep resistance (error value < 0.90%). Overall, the creep test results demonstrate that the sensor retains its measurement accuracy over a prolonged period, making it suitable for long-term monitoring applications.

A Programmable Temperature and Humidity Test Chamber (AP-HX-150D6) with a temperature range of −60°C to 150°C, an accuracy of 0.3°C, and a resolution of 0.1°C was used to evaluate the temperature compensation ability of the tilt sensor, considering the high-temperature sensitivity of the FBG. The tilt sensor was placed in the temperature chamber and connected to the FBG interrogator using a fiber optic jumper wire. The temperature was varied from 30°C to 70°C in 10°C increments. The temperature was kept for 120 minutes for each temperature point and a recording sampling frequency of 1 Hz. The temperature compensation performance testing system is shown in Fig. 11 (color online). After subjecting the tilt sensor to different temperature settings, the data was recorded and analyzed. This experimental setup allowed for the evaluation of how the FBG tilt sensor responded to temperature variations, enabling the assessment of its temperature compensation performance. As the temperature was varied from 30°C to 70°C, the wavelength shifts curves of FBG1 and FBG2 almost coincide as illustrated on the left-hand Y-axis of Fig. 12 (color online). Furthermore, the right-hand Y-axis shows the output of the wavelength shift difference between FBG1 and FBG2. As evident in the graph, the wavelength shifts difference remains approximately around zero. The uniformity of the wavelength drift between FBG1 and FBG2, as shown in Fig. 12, indicates that the temperature compensation mechanism is functioning effectively (error value < 0.90%). The close-to-zero drift reflects the fact that both FBGs are experiencing similar thermal effects, with their wavelength shifts canceling each other out. This is an important feature of the sensor design, as it ensures that the tilt measurements are not affected by temperature variations, thereby enhancing the sensor’s accuracy and stability in environments with fluctuating temperatures. This phenomenon highlights the successful implementation of temperature compensation, as well as the suitability of the FBG positioning and bonding method for achieving precise and stable performance.

The developed optimized tilt sensor system has been installed in an underground pipeline project as shown in Fig 13(a) (color online). The pipeline, filled with cooling water and supported by a steel structure, carries a significant load due to its large weight. The sensor was installed on two locations of the horizontal steel structure where maximum tilt occurs. Afterward, it was secure in place using tape. The monitoring system consists of two sensors connected to the FBG interrogator by a fiber optic jumper, which is then linked to a computer for displaying real-time wavelength shifts, as shown in Fig. 13(b)−13(d) (color online). The sensors are labeled as 1 and 2. Monitoring the deformation and tilt of the supporting structure is crucial for ensuring engineering safety, and the sensor’s enhanced sensitivity provides accurate and reliable measurements.

Over a six-month period, the steel structure supporting the pipeline was continuously monitored, with wavelength shifts recorded by the FBG interrogator at a frequency of 1 Hz. Figures 14(a) and 14(b) (color online) show the tilt angle curves for the two sensors during this period. Evidently from the graph at certain points, sensor 1 recorded minimum and maximum tilt angles of −10.7° and 10.4°, respectively, while sensor 2 recorded minimum and maximum tilt angles of −7.1° and 8.5°. These large tilt measurements are primarily due to external shocks from the heavy machinery powering the cooling water system for the pipeline, which induce sharp tilting responses in the support structure. Additionally, it is evident that the continuous operation of this heavy machinery generates persistent vibrations, resulting in oscillations in the sensor readings. This highlights the sensor’s sensitivity to environmental conditions, particularly in vibrating environments. While the sensor is optimally suited for applications in stable, non-vibrating conditions, its adaptability in dynamic settings can be enhanced. For instance, signal processing methods, such as those used in this research, allow effective isolation of vibration-induced noise, ensuring accurate measurement of tilt angles. Also, to mitigate the impact of such vibrations, design modifications, such as introducing damping materials within the sensor, have been explored in previous studies^[22] and shown to reduce oscillatory effects on the sensor’s mass block. Under normal operational conditions, the real-time tilt angle curve for the vibrations typically ranges from about −5° to 5°. To accurately interpret the data, the coupled signal was decomposed to separate the tilt angle signal from the vibration signal. During vibrational periods, the central value of the rapid angle fluctuations can be used as the primary measurement data for the tilt sensor. The extraction process for this central value from the vibration signal is also shown in Figure 14(a). The symmetric spread around the central line indicates stable sensor performance and reliable data capture over the six months, without any significant drift, even in the presence of vibrational forces. Further, the two central values are extracted and displayed in Fig. 15. The central trend line, derived from signal decomposition, shows values close to zero degrees, corresponding to the baseline tilt angle influenced by the environmental vibrations. These central values represent the equilibrium position of the structure when subjected to minor vibrations from the surrounding heavy machinery. To provide a more detailed view, the decomposed vibration signal for one specific hour (225 h to 226 h) from the six-month period was amplified, as illustrated in Figure 14(b). It can be observed that the tilt angle oscillations remained within a range of −5° to 5°, typical for environments with continuous mechanical activity, where the support structure experiences repetitive shifts in tilt in response to nearby operational equipment. As noted, mechanical disturbances generate transient forces that temporarily affect sensor readings, causing the tilt sensor to register tilts within that range. Therefore, the observed deviations are due to the operational conditions rather than actual structural shifts, as the structure’s tilt remained stable and uniform, with the average tilt centering around zero. This stability confirms that the structure met the monitoring requirements effectively.

This paper presented an extension of the work initially introduced in Ref. [21], further enhancing the sensitivity of a femtosecond FBG tilt sensor through structural design optimization. The use of custom-inscribed FBGs via femtosecond laser writing provides key advantages, including enhanced sensitivity, localized writing capabilities, and improved performance in challenging environments, making them particularly suitable for SHM applications. FEA was employed in the optimization process to address minor deviations from the ideal linear relationship between strain and the distance from the neutral axis in a bending beam, as stated in static mechanics. The study identified an optimal distance of 4.4 mm from the neutral axis to produce the maximum strain, as shown in the curvilinear graph from the FEA study. Two FBGs with different central wavelengths were prestressed and assembled on the optimized sensor cantilever. Experimental results showed that the optimized sensor achieved a sensitivity of 129.95 pm/° and a linearity of 0.9997, outperforming the initial design. This enhanced sensitivity improves accuracy and reliability, crucial for applications requiring high precision. Consequently, while both designs are functional, the optimized sensor design significantly enhances performance in critical applications, enabling more accurate tilt angle detection and measurement due to its improved sensitivity. Successfully employed in an underground pipeline project, the sensor monitored the deformation and tilt of a steel structure, demonstrating practical value in ensuring engineering safety in challenging environments.